Vague Ideals and Normal Vague Ideals in Γ-Semirings

Abstract

The notions of left(right) vague ideal and normal left(right) vague ideals of Γ-semirings with membership and non-membership functions taking values in unit interval of real numbers are introduced which generalize the existing notions left(right) fuzzy ideal and normal left(right) fuzzy ideal of Γ-semiring and studied various properties. Further we proved, a non-constant maximal element in set of all normal left (right) vague idea of a Γ-smearing takes only two values [0,0] and [1,1].

Mathematics Subject Classification: 08A72, 20N25, 03E72.